The Earth: directions, latitude and longitude

Navigation · Chapter 1 · DGCA CPL and ATPL

The shape of the Earth, which way it spins, how pilots give directions, and the circles we draw on it to say exactly where anything is.

Remember

What shape is the Earth, and how big?

Shape and size

  • Almost a perfect ball From space, the Earth looks like a perfect ball. It very nearly is. Drag the picture to turn it.
  • Spinning made it fat round the middle Long ago the Earth was a spinning cloud of gas and dust. Spinning throws the middle outwards, like water flying off a turning wheel. So the middle, round the equator, bulged out, and the top and bottom, the poles, went a little flat. Spin it faster and watch.
  • How flat? Only 1/300 This flattening is called compression. For the Earth it is about 1/300, or 0.3 %. Across the equator the Earth is about 6 888 NM wide. Pole to pole it is 23 NM (43 km) less. Drawn true to size, you could never see it. The name for this shape is an oblate spheroid.
  • Not even neat: the geoid Measured very closely, the Earth is also a little lumpy, and slightly pear-shaped: fattest just south of the equator. It is not a sphere, and not a neat squashed ball either. The only good name is "Earth-shaped", which is what geoid means. Here the bumps are drawn hundreds of times too big. The real ones are only tens of metres.
  • One shape for the whole world: WGS 84 Countries built their own models of this shape. The UK used one, France another, and their maps could disagree by about 200 m. GPS and aircraft computers (FMS) need one model everywhere, so ICAO made WGS 84 the one model everybody uses.
  • For every exam sum: a perfect ball In exam sums, forget the squash and the lumps: treat the Earth as a perfect sphere. All the way round it measures 21 600 NM, which is 40 000 km. Watch the equator being measured.

Where are the poles, and which way does the Earth turn?

Poles and the spin

  • The poles: the ends of the spin The Earth spins all the time, round an imaginary line through its centre: the axis. The two ends of the axis are the poles. The axis really leans over by 23½°; you will use that in the Time chapter. Here we draw it standing straight.
  • Which way does it turn? It always turns the same way, and navigators call that way east. That is why the Sun rises in the east: your side of the Earth is turning towards it.
  • Face east: north is on your left Stand on the equator and face east, the way the Earth turns. The pole on your left is the North Pole, and going towards it is north. The opposite way is south. Behind you is west.
  • Look down on the North Pole Fly up above the North Pole and look down. The Earth turns anticlockwise.
  • Look up at the South Pole From below the South Pole, the very same spin looks clockwise. Nothing changed: you are looking from the other end.

How do pilots say a direction?

Directions in degrees

  • Four main directions North, east, south and west are the four cardinal points. North is the way to the North Pole. East is the way the Earth turns.
  • Four more in between Halfway between them are north-east, south-east, south-west and north-west: the quadrantal points. Sailors split these again and again (north-north-east and so on). That is too clumsy for flying.
  • Pilots count 360 degrees Instead, pilots count degrees round a circle, clockwise from north. North is 000°, east 090°, south 180°, west 270°, and on round to 360°, which is north again. Drag the needle.
  • True direction When "north" means the real North Pole, the direction is called true, and written with (T). So due east is 090°(T), and due west is 270°(T).
  • Always three figures A direction is always said with three figures: 090°, never 90°. Why? On a crackly radio, "27" might have been 027°, 270°, 127° or 271°. Three figures every time stops the mix-up. Runways are the one exception: runway 27 points about 270°. (Runways use magnetic north, not true.)
  • The way back: the reciprocal The exact opposite direction is the reciprocal: add or take away 180°. Fly out on 070° and 250° brings you home. A runway pointing 341° has 161° at its other end. Drag the needle: the dashed arrow always points back.

How do you say where a place is on a ball?

From paper to ball

  • On paper, two numbers fix a point On graph paper you find a point with two numbers: how far across (x) and how far up (y). Both are measured from two starting lines that cross at 90°. Here the "paper" is a flat map of the world.
  • But the Earth is a ball Now wrap the map round a ball. The straight lines bend into circles, and "how far across" becomes an angle. Watch it wrap, or drag the slider.
  • Two starting circles So on a ball we measure angles from two starting circles, the way x and y are measured from two lines. The yellow circle round the middle and the pink one from pole to pole are those two. Next: what kind of circles they are.

What is a great circle?

Great and small circles

  • Cut a ball, get a circle Slice a ball with a flat knife. Wherever you cut, the edge of the cut is a circle. Move the knife and tilt it. Every cut makes a circle.
  • Through the centre: a great circle Now cut right through the centre. This gives the biggest circle the ball can have. Its centre is the Earth's centre and its radius is the Earth's radius. That is a great circle. It cuts the Earth into two equal halves.
  • Anywhere else: a small circle Cut anywhere else and the circle is smaller, and its centre is not the Earth's centre. Any circle on the Earth that is not a great circle is a small circle.
  • The shortest way between two places The shortest path over the Earth between two places runs along the great circle through them, taking the shorter way round. Delhi to New York: the pink great circle runs up near the North Pole. The blue dashed line keeps one steady heading: a rhumb line. It is much longer.
  • Only one great circle… usually Through any two places there is just one great circle. The exception: two places exactly opposite each other, like the two poles. Then endless great circles pass through both.

Which lines on the globe have names?

The lines with names

  • The equator The equator is the great circle at 90° to the axis, halfway between the poles. It splits the Earth into the northern and southern hemispheres. It is the starting line for latitude: the "x line" of our graph paper.
  • Meridians A meridian is half a great circle, running from the North Pole to the South Pole. Every meridian runs exactly north–south (true north), and it crosses the equator at 90°.
  • A meridian and its anti-meridian Follow a meridian over the pole and down the far side. That other half is its anti-meridian. Together they make one whole great circle. Every great circle through the poles is a meridian plus its anti-meridian.
  • The prime meridian One meridian was chosen as the start: the one through Greenwich, in London. It is the prime meridian, 0°. It is the starting line for longitude: the "y line" of our graph paper.
  • Parallels of latitude Circles round the Earth that are parallel to the equator are parallels of latitude. They run east–west. Their centres sit on the axis, above or below the Earth's centre, so they are small circles. Of all the parallels, only the equator is a great circle.
  • The graticule All the meridians and parallels together make a net, like the squares on graph paper. This net is the graticule. With it, any place on Earth can be named exactly.

How are the angles measured?

Degrees, minutes, seconds

  • Angles in degrees Latitude and longitude are angles, not distances. A full turn is 360 degrees (360°).
  • One degree = 60 minutes For more detail, each degree is split into 60 minutes of arc, written ′. These are not minutes of time: just smaller pieces of angle.
  • One minute = 60 seconds Each minute is split again into 60 seconds of arc, written ″. So 1° = 60′ = 3 600″.
  • Where each is used Positions use degrees, minutes and seconds: 28°34′12″N. Directions use degrees, sometimes with decimals: 090°, 123.5°.

What is latitude?

Latitude

  • Cut the Earth in half Latitude says how far north or south of the equator a place is. To see it, cut the Earth in half from pole to pole, along a meridian, and look at the cut face.
  • An angle at the centre Draw a line from the centre to a place, A. The angle between that line and the equator, at the centre, is A's latitude. It is the same as the arc along the meridian, from the equator up to A. Drag A.
  • From 0° to 90°, north or south On the equator the latitude is 0°. It grows to 90°N at the North Pole and 90°S at the South Pole. So latitude never goes past 90°, and it always says N or S.
  • One latitude, one ring Every place with the same latitude sits on one ring round the Earth: a parallel of latitude. "40°N" names a whole ring. Longitude will pick out one spot on it.
  • Four special parallels Four parallels have names. They come from the 23½° lean of the axis (more in the Time chapter). Tropic of Cancer 23½°N and Tropic of Capricorn 23½°S. Arctic Circle 66½°N and Antarctic Circle 66½°S.

Which latitude is printed on charts?

The latitude on your chart

  • Measured from the centre The latitude we just drew used the centre of the Earth. It is called geocentric latitude. Here the Earth is drawn far too squashed, so you can see what comes next.
  • Measured from the ground Stand at P. A line at 90° to the ground, "straight up", is called the normal. On a squashed Earth it does not pass through the centre. The angle between the normal and the equator is geodetic (also called geographic) latitude. Move P.
  • How big is the gap? On the real Earth the two are almost the same: no gap at the equator or the poles, and the biggest gap at about 45°, about 11.6 minutes.
  • Charts use geodetic latitude Every latitude printed on a navigation chart is geodetic.

What is longitude?

Longitude

  • Look down on the North Pole Longitude says how far east or west of Greenwich a place is. Look down on the North Pole: the meridians spread out like the spokes of a wheel. Greenwich is at the bottom.
  • An angle at the pole Pick a meridian. The angle at the pole between Greenwich and that meridian is its longitude. It is the same as the arc along the equator from Greenwich to the meridian. Turn it.
  • East to the right, west to the left From here the Earth turns anticlockwise, and east is the way it turns. So east is to the right of Greenwich, west to the left. Write longitude with three figures and E or W: 040°E, 074°W.
  • Up to 180° Longitude goes up to 180° each way. 180°E and 180°W are the same meridian, right opposite Greenwich: the Greenwich anti-meridian. Greenwich itself is 000°, neither east nor west.
  • A trap at 180° Now stand on the 180° meridian (it is at the bottom of the picture). East is still 090°, the way the Earth turns. But the eastern longitudes, like 170°E, now sit on your west side, and the western ones on your east side. Trust the numbers, not the side.

How do you find a place from its latitude and longitude?

Finding a place

  • Start at the cross Every position is counted from two starting lines: the equator (yellow) and the Greenwich meridian (pink). They cross in the sea off West Africa, at 0°, 000°. We always start from this cross.
  • Example 1 · 20°N 000° 20°N 000° means 20° north of the equator, and no distance east or west. From the cross, go 20° north, up the Greenwich meridian. The light ring is the 20°N parallel: every place on it is 20° north.
  • Example 2 · 00° 040°E Now a place on the equator: 00° (not north or south at all) and 040°E. From the cross, go 40° east along the equator. The light half-ring is the 040°E meridian: every place on it is 040°E.
  • Example 3 · 20°N 040°E Now both. First go 20° north up the Greenwich meridian. Then turn and go 40° east along the 20°N ring. The point sits where the 20°N ring and the 040°E meridian cross. That is why it is there.
  • Example 4 · 30°S 060°W S means south of the equator; W means west of Greenwich. From the cross go 30° south, down the Greenwich meridian. Then go 60° west along the 30°S ring.
  • Example 5 · a real place Mumbai is 19°N 073°E: 19° north of the equator, then 73° east of Greenwich.

What happens to longitude as you walk east or west?

Walking east and west

  • Walking east, away from Greenwich Stand at 030°E on the equator and walk 20° east. You are moving away from Greenwich, so the number grows: 30 + 20 = 50. You are at 050°E.
  • Walking west, towards Greenwich From 030°E walk 20° west. Now you are moving towards Greenwich, so the number shrinks: 30 − 20 = 10. You are at 010°E.
  • Walking past Greenwich From 030°E walk 40° west. The first 30° bring you to Greenwich, 000°. You still have 10° to go, and now you are on the west side: 010°W.
  • Walking past 180° At the back of the Earth is the 180° meridian. From 160°E walk 40° east. The first 20° bring you to 180°. You still have 20° to go, now on the west side, where the numbers count down from 180: 180 − 20 = 160°W.
  • The rule Ask two things every time. Am I walking away from Greenwich (the number grows) or towards it (the number shrinks)? And do I pass 000° or 180° on the way? If so, count up to it, then carry on with what is left on the other side.

How far apart are two longitudes?

Change of longitude

  • Same side: subtract How many degrees of longitude lie between two places, A and B? This is the change of longitude, "ch long". If both are east, or both are west, subtract: 090°W and 060°W are 30° apart.
  • Opposite sides: add If one is east and one is west, add them: 015°W and 025°E are 40° apart, across Greenwich.
  • Opposite sides near 180°: measure from 180° 170°E and 165°W are both near the top, 180°. The short way between them goes through 180°, not through Greenwich. So measure each one from 180°: 170°E is 10° from it, 165°W is 15° from it. Add the two pieces: 10 + 15 = 25°.
  • Try any two Move A and B. The rule in the corner changes as you go.

Solve it: change of longitude

Solve it: ch long

  • Solve it: change of longitude
  • chlong

How are latitude and longitude different?

Pineapple and orange

  • Parallels: slices of a pineapple Parallels of latitude never meet. They are stacked like the slices of a pineapple. Pull the slices apart.
  • Meridians: segments of an orange Meridians all start at the North Pole, spread widest at the equator, and meet again at the South Pole, like the segments of an orange. So the gap between two meridians shrinks as you go towards a pole.

How do you write where a place is?

Writing a position

  • Latitude first, then longitude To give a position, say the latitude first and the longitude second. Mumbai is about 19°N 073°E: 19° up from the equator, and 73° east of Greenwich.
  • Adding minutes For more detail, add minutes. A point near Delhi airport is 28°34′N 077°06′E, written short as 2834N 07706E. Read it as 28 degrees 34 minutes north, 77 degrees 6 minutes east.
  • And seconds Exact to the second: 28°34′12″N 077°06′15″E, written 283412N 0770615E.

How do angles turn into nautical miles?

Minutes into miles

  • A mile made to fit the Earth The nautical mile was chosen to fit the Earth: one minute of arc along a great circle is 1 NM, about 6 080 feet. Today it is fixed at exactly 1 852 metres.
  • Up and down a meridian Meridians are great circles, so every minute of latitude is 1 NM, and every degree is 60 NM. 2000N to 2010N on one meridian is 10 minutes: 10 NM.
  • All the way round: 21 600 NM A whole great circle is 360° × 60 = 21 600 minutes, so 21 600 NM. That is the number from Lesson 1.
  • Longitude shrinks Along the equator, a minute of longitude is 1 NM too. Nowhere else. Parallels get smaller towards the poles, so a minute of longitude gets shorter: about 0.64 NM at 50°, half a mile at 60°.

The shape of the Earth and the nautical mile

Worked examples

  • How flat is the Earth? Compare the two diameters: 6 888 NM across the equator and 6 865 NM pole to pole. The difference over the bigger one is the compression: about 1/300, or 0.3 %.
  • A nautical mile is not the same everywhere One minute of geodetic latitude is longest at the poles, where the Earth is flattest: about 1 862 m. At the equator about 1 843 m; at 45° the standard 1 852 m.
  • A kilometre in feet From the original metre: equator to pole = 10 000 km. So 1 km = 3 280 ft (1 m = 3.28 ft).

How exact is a written position?

How exact is a position?

  • 2834N: to the nearest minute A position also says how exact it is. 2834N means "nearer to 2834 than to 2833 or 2835": to the nearest minute. A minute of latitude is 1 NM, so the place is inside a box about 1 NM across. Fine for flying en route.
  • 2834.2N: one decimal A tenth of a minute: about 600 ft, or 185 m. This is how GPS, FMS and inertial systems show position.
  • 28°34′12″N: seconds To the nearest second: about 100 ft, or 30 m. Used on airfield charts.
  • 12.4″: a tenth of a second About 10 ft, or 3 m. Used to place a precision landing aid like the ILS.
  • 12.37″: a hundredth About 1 ft, or 30 cm. Used when checking (calibrating) an ILS.

What is the point exactly opposite a place?

Opposite points

  • Straight through the centre The point exactly opposite a place is on the far side of the Earth. Draw a line from the place, straight through the centre, and out the other side. Opposite the North Pole is the South Pole.
  • On the equator Opposite the cross (0°, 000°) is 0°, 180°: still on the equator, but half-way round the world.
  • The longitude rule Opposite 040°E is 140°W. The two numbers always add up to 180 (40 + 140 = 180), and E becomes W. So the opposite longitude is 180 minus the number, with E and W swapped.
  • The latitude rule Opposite a northern place is a southern one, the same distance from the equator: 30°N becomes 30°S. So opposite 30°N 000° is 30°S 180°.
  • Both together Opposite 40°N 060°E: the latitude 40°N becomes 40°S. The longitude: 180 − 60 = 120, and E becomes W: 120°W. So the opposite point is 40°S 120°W.

Where is a great circle's highest point?

Great circle vertices

  • A tilted great circle Here is a great circle that is tilted: it climbs to 30°N on one side of the Earth and dips to 30°S on the other. Its most northerly point is the northern vertex; its most southerly point is the southern vertex.
  • The vertices are opposite points The two vertices are exactly opposite each other, straight through the centre. So use the opposite-point rules from the last lesson. 30°N 000° → 30°S 180°. They are half a great circle apart: 10 800 NM.
  • Flat at the top At a vertex the circle runs exactly east–west, like a ball at the top of its throw. An aircraft there flies 090° (east) or 270° (west).
  • Where it crosses the equator Half-way between the top and the bottom, the ring crosses the equator: 90° of longitude away from the vertex, once to the east and once to the west. From 000°: 90° east is 090°E, and 90° west is 090°W.
  • The track at the crossings Watch the dial above the aircraft (track, clockwise from north). At the top: 090°. Flying downhill it turns south; by the equator it has turned by the vertex latitude: 090° + 30° = 120°. Past the bottom it climbs again: at the other crossing 090° − 30° = 060°.
  • A harder one Vertex 50°N 030°E. Opposite point: 50°S, and 180 − 30 = 150, E → W: 150°W. Crossings: 30 + 90 = 120°E, and 90° west from 030°E is 30° to 000° plus 60° more: 060°W. Tracks: 090 + 50 = 140° and 090 − 50 = 040°.
  • Try your own Move the vertex and everything follows. Two special cases: a vertex at 90° makes a meridian; a vertex at 0° is the equator itself.

Solve it: a great circle from its vertex

Solve it: vertices

  • Solve it: a great circle from its vertex
  • vertex

Test yourself on chapter 1

Test yourself

  • Eight questions Each answer appears on the globe. Take your time.